Editorial summaries of third-party claims. We do not independently certify mathematical proofs or represent OpenAI or Anthropic.
Imagine moving a very thin needle in every direction while using almost no space. The Kakeya conjecture asks how small such a set can be. An OpenAI system reports a route to resolving this and related questions about waves.
Some puzzles seem to get overwhelmingly harder as they grow. A new AI-generated argument claims that a famous prediction about how quickly this happens is wrong.
Picture a whirlpool spinning ever faster into an increasingly tiny region. Can the equations describing water or air become infinitely intense from a smooth start? OpenAI says its model constructed such an example.
Testing a strategy once leaves room for luck. Repeating the test should reduce the chance of passing every round. Quantum players may share entanglement, so proving the expected improvement requires special care.
The determinant is a familiar way to combine a square matrix. Its cousin, the permanent, sums similar products without alternating signs. That small-looking change leads to a very different computational problem.
A group describes reversible operations and how they combine. One way to understand an infinite group is to imitate small portions using permutations of a finite set. Soficity asks whether increasingly accurate imitations of this kind are always possible.
Connect every pair of people and give each connection a color. How large can the group become before some three people have all three connections in the same color?
Packing identical oranges is familiar in three dimensions. Replace the room by a space with many independent coordinates and the same question becomes much harder: how much of the space can disjoint equal balls occupy?
A graph is a network of points and links. Add enough links and particular patterns become unavoidable. Extremal graph theory asks where that transition occurs.
Take a solid shape without dents and place it on an integer grid. Suppose its center of mass is the only grid point strictly inside. How much volume can the shape have?
Imagine turning a structure into a complicated measuring device. Can you reconstruct the original structure from that device alone, or can different originals produce indistinguishable devices? This is the intuition behind a rigidity question.
Picture a regular grid extended into many dimensions. Given a point between grid points, finding the closest grid point is easy to describe but can be computationally difficult. Even an approximately nearest point may be hard to find.
A communication system adds redundancy so a damaged message can still be recognized. The codewords must remain sufficiently different. How many distinguishable messages fit when every pair needs a minimum separation?
Put many points on paper and connect every pair exactly one unit apart. How many lines can you get? An OpenAI model found examples that beat a long-standing guess about the best arrangement.
Data & governance · provider_announcement
OpenAI will honor a shared robots.txt signal to help website operators communicate their AI training preferences to participating providers.
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OpenAI shares excerpts from court briefs by creators, academics, accessibility advocates, and legal experts, among others, on how fair use supports AI training and innovation.
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Ropes & Gray is developing AI for transactional diligence with OpenAI. Lawyers review grouped documents, summaries, and reports before advising clients.
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OpenAI’s updated Model Spec outlines five core values to guide more capable AI toward sound judgment, human agency, and faithfulness to human intent.
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OpenAI uses layered monitoring to detect frontier model misalignment and unauthorized agent behavior so responders can intervene before incidents escalate.
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How AI might enter the org chart—beneath, beside, and between us.
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OpenAI and ServiceNow expand their partnership to bring OpenAI models and agents into ServiceNow and ServiceNow workflows into ChatGPT and Codex.
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See how Legora uses OpenAI models, ChatGPT, and Codex to accelerate legal workflows, expand contract analysis, and free lawyers to focus on higher-value work.
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OpenAI and Oracle are expanding their partnership to bring business applications and AI agents into ChatGPT and power new Oracle offerings.
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GPT-6 Astra tops Retell’s voice agent benchmark, while Codex helps it reach a $1.6M annual revenue run rate per employee.
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How Greptile uses GPT-6 Astra to test user workflows, Daybreak to strengthen security, and Codex to reduce rework.
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CodeRabbit uses GPT-6.1 Sol to investigate security risks across complex codebases. Its security agent helps developers review findings and proposed fixes.
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